Subgroups — #11760903

Order 1056.

216 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₁×D₁₂	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×D₄₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#63140	C₂	1	4	yes	maximal, complemented
4	C₄×Dic₃₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#66993	—	3	1	no	maximal, Hall
6	C₂²×D₃×C₁₁	C₂²	1	2	yes	—
7	C₂²×C₃×D₁₁	C₂²	1	2	yes	—
8	C₂×C₃×C₄×C₁₁	C₂²	1	1	yes	characteristic
9	C₂×Dic₃₃	C₂²	1	2	yes	—
10	C₁₁×D₁₂	—	2	2	no	—
11	C₃×D₄₄	—	2	2	no	—
12	#63140	—	2	8	no	—
13	C₂×D₄×C₁₁	—	3	1	no	—
14	C₂×C₂²⋊D₁₁	—	3	4	no	—
15	C₂×D₄₄	D₃	1	1	yes	characteristic, complemented
16	C₄×Dic₁₁	—	3	1	no	—
17	C₂²×C₃×C₁₁	C₂³	1	1	yes	characteristic
18	C₂×D₃×C₁₁	—	2	4	no	—
19	C₂×D₃×C₁₁	—	2	2	no	—
20	C₂×C₃×D₁₁	—	2	4	no	—
21	C₂×C₃×D₁₁	—	2	2	no	—
22	C₃×C₄×C₁₁	D₄	1	2	yes	complemented
23	Dic₃₃	D₄	1	4	yes	complemented
24	#940	—	11	1	no	maximal, Hall
25	C₂³×C₁₁	—	3	2	no	—
26	C₂²×D₁₁	C₂×D₃	1	2	yes	—
27	D₄×C₁₁	—	6	2	no	—
28	C₂×C₄×C₁₁	C₂×D₃	1	1	yes	characteristic
29	C₂²⋊D₁₁	—	6	8	no	—
30	C₂×Dic₁₁	—	3	2	no	—
31	D₄₄	—	2	2	no	—
32	C₂×C₃×C₁₁	C₂×D₄	1	2	yes	—
33	C₂×C₃×C₁₁	C₂×D₄	1	1	yes	characteristic
34	C₃×D₁₁	—	4	2	no	—
35	D₃×C₁₁	—	4	2	no	—
36	C₂×C₃×D₄	—	11	1	no	—
37	C₂×#67	—	11	4	no	—
38	C₂×D₁₂	D₁₁	1	1	yes	characteristic, complemented
39	C₄×Dic₃	—	11	1	no	—
40	C₂²×C₁₁	—	6	4	no	—
41	C₂²×C₁₁	—	6	2	no	—
42	C₂²×C₁₁	C₂²×D₃	1	1	yes	characteristic
43	C₂×D₁₁	—	2	4	no	—
44	C₂×D₁₁	—	2	2	no	—
45	C₄×C₁₁	#67	1	2	yes	complemented
46	Dic₁₁	—	3	4	no	—
47	C₃×C₁₁	#127	1	1	yes	characteristic, complemented, Hall
48	#127	—	33	1	no	Sylow
49	C₂³×C₃	—	11	2	no	—
50	C₂²×D₃	C₂×D₁₁	1	2	yes	—
51	C₃×D₄	—	22	2	no	—
52	C₂×C₃×C₄	C₂×D₁₁	1	1	yes	characteristic
53	#67	—	22	8	no	—
54	C₂×Dic₃	—	11	2	no	—
55	D₁₂	—	2	2	no	—
56	C₂×C₁₁	—	12	2	no	—
57	C₂×C₁₁	D₃×D₄	1	2	yes	—
58	C₂×C₁₁	C₂×#67	1	1	yes	characteristic
59	D₁₁	—	4	2	no	—
60	C₂×D₄	—	3	1	no	—
61	C₂×D₄	—	11	1	no	—
62	C₂×D₄	—	33	4	no	—
63	C₄²	—	33	1	no	—
64	C₂²×C₃	—	22	4	no	—
65	C₂²×C₃	—	22	2	no	—
66	C₂²×C₃	C₂²×D₁₁	1	1	yes	characteristic
67	C₂×D₃	—	2	4	no	—
68	C₂×D₃	—	2	2	no	—
69	C₃×C₄	C₂²⋊D₁₁	1	2	yes	complemented
70	Dic₃	—	11	4	no	—
71	C₁₁	#940	1	1	yes	characteristic, complemented, Sylow
72	C₂³	—	3	2	no	—
73	C₂³	—	11	2	no	—
74	D₄	—	6	2	no	—
75	D₄	—	22	2	no	—
76	D₄	—	66	8	no	—
77	C₂×C₄	—	33	2	no	—
78	C₂×C₄	D₃×D₁₁	1	1	yes	characteristic
79	C₂×C₃	—	44	2	no	—
80	C₂×C₃	D₄×D₁₁	1	2	yes	—
81	C₂×C₃	C₂×C₂²⋊D₁₁	1	1	yes	characteristic
82	D₃	—	4	2	no	—
83	C₂²	—	6	4	no	—
84	C₂²	—	6	2	no	—
85	C₂²	—	22	4	no	—
86	C₂²	—	22	2	no	—
87	C₂²	C₂×D₃×D₁₁	1	1	yes	characteristic
88	C₄	—	33	4	no	—
89	C₄	#63140	1	2	yes	complemented
90	C₃	#66993	1	1	yes	characteristic, complemented, Sylow
91	C₂	—	12	2	no	—
92	C₂	—	44	2	no	—
93	C₂	#10587239	1	2	yes	—
94	C₂	C₂×#63140	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂×D₃×D₁₁
commutator, socle, cosocle	C₂²×C₃×C₁₁	C₂³
Fitting	C₂×C₃×C₄×C₁₁	C₂²
hypercenter	C₂×C₄	D₃×D₁₁
hypocenter	C₃×C₁₁	#127
LCS	G ▷ C₂²×C₃×C₁₁ ▷ C₃×C₁₁
UCS	C₁ ◁ C₂² ◁ C₂×C₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×C₁₁×D₁₂	C₂	semidirect
2. C₂×C₃×D₄₄	C₂	semidirect
3. C₂×#63140	C₂	semidirect
4. C₄×Dic₃₃	C₂	semidirect
15. C₂×D₄₄	D₃	semidirect
22. C₃×C₄×C₁₁	D₄	semidirect
23. Dic₃₃	D₄	semidirect
38. C₂×D₁₂	D₁₁	semidirect
45. C₄×C₁₁	#67	semidirect
47. C₃×C₁₁	#127	semidirect
69. C₃×C₄	C₂²⋊D₁₁	semidirect
71. C₁₁	#940	semidirect
89. C₄	#63140	semidirect
90. C₃	#66993	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₁×D₁₂	2
C₂×C₃×D₄₄	2
C₂×#63140	2
C₄×Dic₃₃	2
#66993	3
#940	11